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College Algebra
Linear Systems
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Verify that the values of the variables listed are solutions of the system of equations.
1)
x+y=3
x-y=7
x = 5, y = -2
A) solution
2)
B) not a solution
2)
x+y=5
x-y=3
x = -4, y = 1
A) solution
B) not a solution
Solve the system of equations by substitution.
3)
x + y = -3
x - y = 16
A) x = 3, y = -9.5; (3, -9.5)
C) x = 6.5, y = 9.5; (6.5, 9.5)
4)
5)
6)
1)
3)
B) x = 3, y = 6.5; (3, 6.5)
D) x = 6.5, y = -9.5; (6.5, -9.5)
4)
x + 6y = 6
9x - 7y = -7
A) x = 1, y = 0; (1, 0)
C) x = 0, y = 0; (0, 0)
B) x = 0, y = 1; (0, 1)
D) x = 1, y = 1; (1, 1)
5)
5x + 6y = -1
2x
= -10
A) x = -4, y = 0; (-5, 0)
C) x = -5, y = 4; (-5, 4)
B) x = 4, y = -5; (4, -5)
D) x = -5, y = -4; (-5, -4)
6)
5x + 3y = 80
2x + y = 30
A) x = 10, y = 0; (10, 0)
C) x = 0, y = 0; (0, 10)
B) x = 0, y = 10; (0, 10)
D) x = 10, y = 10; (10, 10)
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Solve the system of equations by elimination.
7)
4x + 28y = 28
6x - 7y = -7
A) x = 0, y = 1; (0, 1)
C) x = 1, y = 1; (1, 1)
8)
9)
7)
B) x = 0, y = 0; (0, 0)
D) x = 1, y = 0; (1, 0)
8)
x + y = -1
x - y = 13
A) x = 6, y = -7; (6, -7)
C) x = 1, y = 6; (1, 6)
B) x = 6, y = 7; (6, 7)
D) x = 1, y = -7; (1, -7)
9)
7
x - y = 10
12
5
x + 2y = 11
9
10)
A) x = -16, y = -
1
1
; -16, 2
2
B) x = 18, y =
1
1
; 18,
2
2
C) x = -18, y = -
1
1
; -18, 2
2
D) x = 16, y =
1
1
; 16,
2
2
10)
5x + 3y = 80
2x + y = 30
A) x = 10, y = 10; (10, 10)
C) x = 0, y = 0; (0, 0)
Find the value of the determinant.
11) 3 8
79
A) 29
B) x = 0, y = 10; (0, 10)
D) x = 10, y = 0; (10, 0)
11)
B) -29
C) 83
D) -39
12) 12 -7
-4 3
A) 8
Solve for x.
13) 8 x = 32
2 5
A) -4
Find the value of the determinant.
-3 5 5
14) 5 3 3
3 -4 5
A) 106
12)
B) -8
C) 64
D) 4
13)
B) 4
C) -3
D) 3
14)
B) 306
C) -306
2
D) -396
2 4 5
15) 2 4 1
1 1 1
A) 52
16)
15)
B) -16
C) 8
D) -8
-2 5 4
3 -2 1
1 6 -3
A) -12
16)
B) 80
C) -90
D) 130
Solve the system of equations using Cramer's Rule if it is applicable. If Cramer's Rule is not applicable, say so.
17) 6x + 3y = -6
17)
4x + y = -10
A) x = 4, y = -6; (4, -6)
B) x = -4, y = 6; (-4, 6)
C) x = -6, y = -4; (-6, -4)
D) x = 6, y = -4; (6, -4)
18)
4x + 2y = 42
4x + 3y = 51
A) x = 6, y = 9; (6, 9)
C) x = -6, y = -9; (-6, -9)
18)
B) x = 9, y = 6; (9, 6)
D) x = -9, y = 6; (-9, 6)
6x - 8y = 3
19) 24x - 32y = 9
20)
21)
22)
19)
A) not applicable
B) x = 3, y = 9; (3, 9)
C) x = 4, y = 3; (4, 3)
D) x =
8x + 6y - z = 46
x - 3y + 6z = 51
4x + y + z = 33
A) x = 7, y = -1, z = 8; (7, -1, 8)
C) x = 6, y = -1, z = -8; (6, -1, -8)
2
3 2
3
,y=; ,5
10 5
10
20)
B) x = 1, y = 8, z = 1; (1, 8, 1)
D) x = 6, y = 1, z = 8; (6, 1, 8)
21)
x - y + 4z = 4
2x
+ z =0
-x + y - 4z = -8
A) x = 4, y = -4, z = 0; (4, -4, 0)
C) not applicable
B) x = 0, y = 0, z = -4; (0, 0, -4)
D) x = 0, y = -4, z = 0; (0, -4, 0)
9x - 6y + 4z = 61
-6x + 2y - 6z = -52
-5x - 8y - 9z = -86
A) x = 10, y = 2, z = 1; (10, 2, 1)
C) x = 4, y = 1, z = 4; (4, 1, 4)
22)
B) x = 9, y = -4, z = -1; (9, -4, -1)
D) x = 9, y = 4, z = 1; (9, 4, 1)
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